Let Evaluate the Line Integral $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$

question 162

Multiple Choice

Let $\mathbf { F } ( x , y , z ) = 2 x y ^ { 3 } z ^ { 4 } \mathbf { i } + 3 x ^ { 2 } y ^ { 2 } z ^ { 4 } \mathbf { j } + 4 x ^ { 2 } y ^ { 3 } z ^ { 3 } \mathbf { k }$ . Evaluate the line integral $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$ along the elliptical path $\mathbf { r } ( t ) = \cos t \mathbf { i } + \sin t \mathbf { j } + \cos t \mathbf { k } , \quad 0 \leq t \leq 2 \pi$ .

• A) \(\pi\)
• B) \(\pi \sqrt { 2 }\)
• C)\(\pi \sqrt { 3 }\)
• D)\(2 \pi\)
• E)\(\frac { \sqrt { 2 } } { 2 } \pi\)
• F)\(\frac { \sqrt { 3 } } { 2 } \pi\)
• G)\(\frac { \pi } { 2 }\)
• H)\(0\)

Recognize the importance of environmental factors and community infrastructure in disease prevention.

Understand the historical development of public health initiatives and their impact on community health.

Analyze the role of government and non-governmental organizations in the advancement of public health.

Identify key figures and their contributions to public health and nursing.

---

Definitions:

Population

The entire group of individuals or items that are the subject of a statistical study.

Confidence Interval

A breadth of numerical ranges, derived from samples' statistical outputs, presumed to enclose an unknown population parameter value.

Significance

A statistical concept indicating the likelihood that an observed effect or relationship is not due to chance, often demonstrated by a p-value.

Null Hypothesis

In statistical testing, the default hypothesis that there is no effect or no difference, and any observed effect is due to chance.